1 Answer
1

$$ x^2 +y^2 = \sec^2(\tan^{-1}(x/y)+\tan^{-1}(y/x))$$
$$ = 1 + \tan^2\left(\tan^{-1}\left(\frac{x/y + y/x}{1-1}\right)\right) = \infty$$
In the last step, I have implicitly taken a left hand limit to arrive at the result. Now This represents(as a locus) a circle with infinite radius which some would say technically is a line. Just like a circle with zero radius(radius tends to 0) is a point.
So the software you are using could be giving weird results due to this anomaly. Unfortunately I do not know how the software plots these functions...